- #1

XcKyle93

- 37

- 0

## Homework Statement

Prove that in a Boolean algebra the cancellation law does not hold; that is, show that, for every x, y, and z in a Boolean algebra, xy = xz does not imply y = z.

## Homework Equations

The 6 postulates of a Boolean Algebra

## The Attempt at a Solution

I am uncertain as to whether or not what I have done is a valid proof. Plus, is there a way to do this using solely the postulates? That's what I initially tried to do, but I drew a blank. I honestly needed a hint for the below.

Suppose that for a Boolean algebra, x = 0, y = 1, z = 0. Then, xy = yz becomes:

0*1 = 1*0

0 = 0

Thus, xy = yz does not imply that y = z, and the cancellation law of multiplication does not hold for a Boolean Algebra.